The band played the recording for an audience just once, at an electronic music festival in London. It reportedly includes distorted guitar, organ sounds, gargling and shouts of "Barcelona!" and "Are you all right?" from McCartney and John Lennon.
McCartney said during a recording session at Abbey Road studios he asked the other members of the band to "just wander round all of the stuff and bang it, shout, play it. It doesn't need to make any sense."
"I like it because it's the Beatles free, going off piste," he told the BBC in a radio interview to be broadcast Thursday. Extracts of the interview were published Sunday in The Observer newspaper.
McCartney said he still had a master tape of the piece and "the time has come for it to get its moment."
McCartney, usually regarded as the most melodically minded Beatle, told the BBC he had a long-standing interest in avant-garde music. He said "Carnival of Light" was inspired by experimental composers John Cage and Karlheinz Stockhausen.
He said he had wanted to include the track on the Beatles' "Anthology" compilation, but was vetoed by his bandmates.
McCartney would need permission from Ringo Starr and the widows of Lennon and George Harrison to release the track.